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It is notable that the cyclotron frequency is independent of the radius and velocity and therefore independent of the particle's kinetic energy; all particles with the same charge-to-mass ratio rotate around magnetic field lines with the same frequency. This is only true in the non-relativistic
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The cyclotron frequency is also useful in non-uniform magnetic fields, in which (assuming slow variation of magnitude of the magnetic field) the movement is approximately helical - in the direction parallel to the magnetic field, the motion is uniform, whereas in the plane perpendicular to the
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For some materials, the motion of electrons follows loops that depend on the applied magnetic field, but not exactly the same way. For these materials, we define a cyclotron effective mass,
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Since the motion in an orthogonal and constant magnetic field is always circular, the cyclotron frequency is given by equality of
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magnetic field the movement is, as previously circular. The sum of these two motions gives a trajectory in the shape of a
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When the charged particle begins to approach relativistic speeds, the centripetal force should be multiplied by the
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that utilizes an oscillating electric field tuned to this resonance to add kinetic energy to charged particles.
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describes the interaction of external forces with charged particles experiencing a
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Note that converting this expression to SI units introduces a factor of the
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Effective mass (solid-state physics) § Cyclotron effective mass
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moving perpendicular to the direction of a uniform magnetic field
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515:. In Gaussian units, the Lorentz force differs by a factor of 1/
421:{\displaystyle f={\frac {\omega }{2\pi }}={\frac {qB}{2\pi m}}}
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Physics by M. Alonso & E. Finn, Addison Wesley 1996.
42:, thus moving on a circular path. It is named after the
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571:{\displaystyle \omega ={\frac {v}{r}}={\frac {qB}{mc}}}
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limit, and underpins the principle of operation of the
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Diagram of a cyclotron orbit of a particle with speed
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190:{\displaystyle \omega _{\rm {c}}={\frac {qB}{mc}}}
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135:{\displaystyle \omega _{\rm {c}}={\frac {qB}{m}}}
858:Calculate Cyclotron frequency with Wolfram Alpha
582:For materials with little or no magnetism (i.e.
844:Ashcroft and Mermin. Solid State Physics. pp12
491:{\displaystyle \omega ={\frac {qB}{\gamma m}}}
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74:(constant magnitude and direction).
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833:Introduction to Solid State Physics
883:. You can help Knowledge (XXG) by
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284:, and the circular path radius
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601:{\displaystyle \mu \approx 1}
54:Cyclotron resonance frequency
804:Electron cyclotron resonance
16:Motion of charged particles
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627:{\displaystyle H\approx B}
950:Accelerator physics stubs
636:magnetic field intensity
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930:Condensed matter physics
799:Ion cyclotron resonance
272:with the particle mass
879:-related article is a
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641:instead of
357:Giving the
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46:, a cyclic
924:Categories
810:References
707:See also:
290:gyroradius
204:Derivation
772:∗
751:ω
740:so that:
726:∗
656:ω
619:≈
593:≈
590:μ
530:ω
480:γ
463:ω
435:cyclotron
410:π
387:π
380:ω
310:ω
299:is then:
154:ω
104:ω
89:CGS units
44:cyclotron
793:See also
509:SI units
84:SI units
875:This
443:helix
881:stub
295:The
58:The
62:or
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754:=
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182:c
179:m
174:B
171:q
165:=
159:c
128:m
124:B
121:q
115:=
109:c
72:B
31:.
29:B
25:v
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